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Roots of rational polynomials
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2597		 Page 1 of 1
Author:  jcapco [ Mon Apr 24, 2017 8:49 am ]
Post subject:  Roots of rational polynomials
Consider this code:

Code:
ring A=0,x,lp;
poly f=(x-3/17)*(x+2/3);


I don't see a straightforward way to find the exact (as rational numbers) roots of f. I looked a bit at the documentation and if I use the command laguerre(f,5,1), I obtain roots up to 5 digits (decimal) precision and not really the rational roots 3/17 and -2/3. Of course I can use factorize(f) and write a code that extracts the rational roots, but I am sure (I hope) there is a cleaner way to do this. Any hints would be much appreciated. Thanks!
Author:  jcapco [ Mon Apr 24, 2017 9:36 am ]
Post subject:  Re: Roots of rational polynomials
So far I am using this procedure. It could exist in some library already?

Code:
//rational roots of a rational polynomial
proc Qroots(poly f)
{
  ideal l = factorize(f,1);
  list ret;
  for (int i=1;i<=size(l);i++)
  {
    if (deg(l[i])==1)
    { //roots are rational
      if (size(l[i])==1) { ret=ret+list(0);}
      else { ret = ret + list(-leadcoef(l[i][2])/leadcoef(l[i][1])); }
    }
  }
return(ret);
}
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